Free
Beginner
6h
Updated 4 months ago
Introduction to Logic: Basics of Mathematical Reasoning
Gain insights into formal logic, propositional logic, and first-order logic. Learn inference rules and master proof construction to sharpen critical thinking and problem-solving skills.
Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to evaluate the validity of reasoning, fostering critical thinking skills. Proficiency in constructing and understanding proofs enhances problem-solving abilities, encourages precision in thought, and promotes clarity in communication.
In this course, you’ll explore propositions and logical connectives in propositional logic. Next, you’ll cover first-order logic, which extends the scope to include variables, quantifiers, and predicates. Next, the rules of inference are discussed which provide the logical steps required to establish the validity of mathematical statements.
After taking this course, you’ll develop the skills to navigate and manipulate logical systems effectively. You’ll also acquire the essential toolkit for constructing rigorous and convincing mathematical proofs—a skill that is pivotal in advanced mathematics, computer science, and other analytical disciplines.
Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to eval...Show More
WHAT YOU'LL LEARN
An understanding of propositional logic
An understanding of first-order logic
An understanding of deductive logic
Familiarity with the structure of mathematical proofs
An understanding of propositional logic
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Content
2.
Propositional Logic
3 Lessons
Unpack the core of propositions, logical equivalence, and propositional calculus in mathematical reasoning.
3.
Basic Operations
11 Lessons
Work your way through basic logical operations and their properties, including conjunctions, disjunctions, and negations.
4.
Propositional Toolkit
4 Lessons
Break down complex ideas in logical identities, tautologies, contradictory propositions, and fundamental logical operations.
5.
Logical Reasoning
9 Lessons
Take a look at logical inference, propositional rules, proofs, common fallacies, and logical puzzles.
6.
Quantifiers and First Order Logic
5 Lessons
Investigate the use of predicates, quantifiers, variables, and negation in logical reasoning.
7.
Quantified Logical Reasoning
4 Lessons
Master the steps to nested quantifiers, negation, logical equivalence, and inference rules in reasoning.
8.
Proving Theorems
5 Lessons
Break down the methods of proving theorems and strategies to avoid common proof errors.
Certificate of Completion
Showcase your accomplishment by sharing your certificate of completion.
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